6,168 research outputs found
Invariants of Triangular Lie Algebras
Triangular Lie algebras are the Lie algebras which can be faithfully
represented by triangular matrices of any finite size over the real/complex
number field. In the paper invariants ('generalized Casimir operators') are
found for three classes of Lie algebras, namely those which are either strictly
or non-strictly triangular, and for so-called special upper triangular Lie
algebras. Algebraic algorithm of [J. Phys. A: Math. Gen., 2006, V.39, 5749;
math-ph/0602046], developed further in [J. Phys. A: Math. Theor., 2007, V.40,
113; math-ph/0606045], is used to determine the invariants. A conjecture of [J.
Phys. A: Math. Gen., 2001, V.34, 9085], concerning the number of independent
invariants and their form, is corroborated.Comment: LaTeX2e, 16 pages; misprints are corrected, some proofs are extende
Non-Newtonian fluid-structure interaction: Flow of a viscoelastic Oldroyd-B fluid in a deformable channel
We analyze the steady non-Newtonian fluid-structure interaction between the
flow of an Oldroyd-B fluid and a deformable channel. Specifically, we provide a
theoretical framework for calculating the leading-order effect of the fluid's
viscoelasticity on the flow rate-pressure drop relation and on the deformation
of the channel's elastic wall. We first identify the characteristic scales and
dimensionless parameters governing the fluid-structure interaction in slender
and shallow channels. Applying the lubrication approximation for the flow and
employing a perturbation expansion in powers of the Deborah number , we
derive a closed-form expression for the pressure as a function of the
non-uniform shape of the channel in the weakly viscoelastic limit up to
. Coupling the hydrodynamic pressure to the elastic
deformation, we provide the leading-order effect of the interplay between the
viscoelasticity of the fluid and the compliance of the channel on the pressure
and deformation fields, as well as on the flow rate-pressure drop relation. For
the flow-rate-controlled regime and in the weakly viscoelastic limit, we show
analytically that both the compliance of the deforming top wall and the
viscoelasticity of the fluid decrease the pressure drop. Furthermore, we reveal
a trade-off between the influence of compliance of the channel and the fluid's
viscoelasticity on the deformation. While the channel's compliance increases
the deformation, the fluid's viscoelasticity decreases it.Comment: 5 figure
Effectively engaging stakeholders and the public in developing violence prevention messages
Background: Preventing family violence requires that stakeholders and the broader public be involved in developing evidence-based violence prevention strategies. However, gaps exist in between what we know (knowledge), what we do (action), and the structures supporting practice (policy). Discussion: We discuss the broad challenge of mobilizing knowledge-for-action in family violence, with a primary focus on the issue of how stakeholders and the public can be effectively engaged when developing and communicating evidence-based violence prevention messages. We suggest that a comprehensive approach to stakeholder and public engagement in developing violence prevention messages includes: 1) clear and consistent messaging; 2) identifying and using, as appropriate, lessons from campaigns that show evidence of reducing specific types of violence; and 3) evidence-informed approaches for communicating to specific groups. Components of a comprehensive approach must take into account the available research evidence, implementation feasibility, and the context-specific nature of family violence. Summary: While strategies exist for engaging stakeholders and the public in messaging about family violence prevention, knowledge mobilization must be informed by evidence, dialogue with stakeholders, and proactive media strategies. This paper will be of interest to public health practitioners or others involved in planning and implementing violence prevention programs because it highlights what is known about the issue, potential solutions, and implementation considerations
Key exchange with the help of a public ledger
Blockchains and other public ledger structures promise a new way to create
globally consistent event logs and other records. We make use of this
consistency property to detect and prevent man-in-the-middle attacks in a key
exchange such as Diffie-Hellman or ECDH. Essentially, the MitM attack creates
an inconsistency in the world views of the two honest parties, and they can
detect it with the help of the ledger. Thus, there is no need for prior
knowledge or trusted third parties apart from the distributed ledger. To
prevent impersonation attacks, we require user interaction. It appears that, in
some applications, the required user interaction is reduced in comparison to
other user-assisted key-exchange protocols
Invariants of Lie Algebras with Fixed Structure of Nilradicals
An algebraic algorithm is developed for computation of invariants
('generalized Casimir operators') of general Lie algebras over the real or
complex number field. Its main tools are the Cartan's method of moving frames
and the knowledge of the group of inner automorphisms of each Lie algebra.
Unlike the first application of the algorithm in [J. Phys. A: Math. Gen., 2006,
V.39, 5749; math-ph/0602046], which deals with low-dimensional Lie algebras,
here the effectiveness of the algorithm is demonstrated by its application to
computation of invariants of solvable Lie algebras of general dimension
restricted only by a required structure of the nilradical.
Specifically, invariants are calculated here for families of real/complex
solvable Lie algebras. These families contain, with only a few exceptions, all
the solvable Lie algebras of specific dimensions, for whom the invariants are
found in the literature.Comment: LaTeX2e, 19 page
The atomic structure of large-angle grain boundaries and in and their transport properties
We present the results of a computer simulation of the atomic structures of
large-angle symmetrical tilt grain boundaries (GBs) (misorientation
angles \q{36.87}{^{\circ}} and \q{53.13}{^{\circ}}),
(misorientation angles \q{22.62}{^{\circ}} and \q{67.38}{^{\circ}}). The
critical strain level criterion (phenomenological criterion)
of Chisholm and Pennycook is applied to the computer simulation data to
estimate the thickness of the nonsuperconducting layer enveloping
the grain boundaries. The is estimated also by a bond-valence-sum
analysis. We propose that the phenomenological criterion is caused by the
change of the bond lengths and valence of atoms in the GB structure on the
atomic level. The macro- and micro- approaches become consistent if the
is greater than in earlier papers. It is predicted that the
symmetrical tilt GB \theta = \q{53.13}{^{\circ}} should demonstrate
a largest critical current across the boundary.Comment: 10 pages, 2 figure
All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1
We construct all solvable Lie algebras with a specific n-dimensional
nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional
maximal Abelian ideal). We find that for given n such a solvable algebra is
unique up to isomorphisms. Using the method of moving frames we construct a
basis for the Casimir invariants of the nilradical n_(n,2). We also construct a
basis for the generalized Casimir invariants of its solvable extension s_(n+1)
consisting entirely of rational functions of the chosen invariants of the
nilradical.Comment: 19 pages; added references, changes mainly in introduction and
conclusions, typos corrected; submitted to J. Phys. A, version to be
publishe
Computation of Invariants of Lie Algebras by Means of Moving Frames
A new purely algebraic algorithm is presented for computation of invariants
(generalized Casimir operators) of Lie algebras. It uses the Cartan's method of
moving frames and the knowledge of the group of inner automorphisms of each Lie
algebra. The algorithm is applied, in particular, to computation of invariants
of real low-dimensional Lie algebras. A number of examples are calculated to
illustrate its effectiveness and to make a comparison with the same cases in
the literature. Bases of invariants of the real solvable Lie algebras up to
dimension five, the real six-dimensional nilpotent Lie algebras and the real
six-dimensional solvable Lie algebras with four-dimensional nilradicals are
newly calculated and listed in tables.Comment: 17 pages, extended versio
Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials
A geometric approach is used to study a family of higher-order nonlinear Abel
equations. The inverse problem of the Lagrangian dynamics is studied in the
particular case of the second-order Abel equation and the existence of two
alternative Lagrangian formulations is proved, both Lagrangians being of a
non-natural class (neither potential nor kinetic term). These higher-order Abel
equations are studied by means of their Darboux polynomials and Jacobi
multipliers. In all the cases a family of constants of the motion is explicitly
obtained. The general n-dimensional case is also studied
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